MG205: Econometrics Theory and Applications

Empirical Exercise 3: Daughters and Legislative Voting

José Ignacio González-Rojas
j.i.gonzalez-rojas@lse.ac.uk

London School of Economics and Political Science

November 10, 2025

Dick Cheney’s Daughter Changed His Vote

A Conservative Republican Supports Gay Rights

Background

  • Vice President under George W. Bush (2001-2009)
  • Reliably conservative voting record
  • Strong Republican party loyalty
  • Expected to oppose LGBTQ rights

The Surprise

  • Daughter Mary came out as lesbian
  • Cheney broke with party on gay marriage
  • Publicly supported same-sex relationships
  • One of few Republicans to do so

Anecdote or systematic pattern? Can children influence parental ideology?

Children May Influence Parental Beliefs on Policy Issues

From Sociology to Political Economy

Sociological Evidence

  • Parents with daughters hold more feminist views (Warner, 1991)
  • Fathers of only daughters support gender equity policies (Warner & Steel, 1999)
  • Effect strongest among educated, high-income parents

Do legislators with daughters vote more liberally on women’s issues (Washington, 2008)?

❗ How do we establish causation?

  • Maybe liberals choose to have more children?
  • Maybe progressive people are more likely to have daughters?

Establishing Random Assignment

Child Gender Must Be Random for Causal Inference

The Identification Challenge

What We Need

  • Random assignment of daughters
  • No selection into treatment
  • Valid control group

What Could Go Wrong

  • China/India: Strong son preference
    • Selective abortion creates bias
    • Gender correlated with parental characteristics
    • Cannot use for causal inference
  • US Context: Need to verify randomness

Without randomisation, we cannot separate causation from correlation

Child Gender Is Random in the United States

Balance Tests Show No Selection Bias

Balance tests across legislator characteristics

US Legislators Have Approximately 50% Daughters

Descriptive Statistics on Family Composition

Average Family Size

  • Mean children: 2.5
  • Mean daughters: 1.3
  • Mean sons: 1.2

Sample: 434 US House Representatives, 105th Congress (1997-1998)

Gender Distribution

  • Proportion daughters: 52%
  • Expected under randomness: 50%
  • Cannot reject equality (\(p = 0.22\))

Child gender operates like nature’s randomised experiment

The Naive Approach Fails

Regressing on Daughters Without Controls Gives Wrong Answer

\(\text{NOW}_{i} = \beta_0 + \beta_1 \cdot \text{daughters}_i + e_i\)

  • \(\hat{\beta}_1 = -2.1\) points per daughter

This suggests daughters make legislators MORE conservative!

But this contradicts:

  • Our theoretical prediction
  • The sociological evidence
  • The Dick Cheney story

What’s going wrong?

Omitting Total Children Creates Confounding

The Causal Structure Reveals the Problem

Conservatives have larger families → More daughters → Negative correlation

Ideology Correlates with Family Size in Our Sample

The Confounding Mechanism

Republicans Have More Children

  • Republicans: 2.6 children on average
  • Democrats: 2.4 children on average
  • Difference: Modest but systematic

Republicans Vote More Conservatively

  • Republicans: 12.0 NOW score
  • Democrats: 73.1 NOW score
  • Difference: 61 points

More children → More daughters → Conservatives have more daughters

This creates spurious negative correlation between daughters and liberal voting

Control for Total Children

Within Family Size Comparisons Isolate Daughter Effect

Two Children Example Shows Clear Pattern

Mean NOW scores by family composition - 2 children

Democrats and Republicans both show increasing NOW scores with more daughters

Pattern Persists for Three Children Families

Consistent Gradient Within Each Party

Mean NOW scores by family composition - 3 children

More daughters → More liberal voting, holding total children constant

Controlling for Total Children Reveals Positive Effect

Omitting total children creates large omitted variable bias

Coefficient on daughters across model specifications

Sign flips from negative to positive when controlling for family size

Each Additional Daughter ⬆️ Liberal Voting by 2.7 Points

\(\text{NOW}_i = \beta_0 + \beta_1 \cdot \text{daughters}_i + \beta_2 \cdot \text{total \# children}_i + \mathbf{X}_i\boldsymbol{\beta} + e_i\)

430 legislators. Controls: race, religion, age, service length
Variable Coefficient Std. Error p-value
Number of daughters 2.72 (1.05) 0.010
Total children -2.83 (0.76) 0.000
Republican -44.87 (2.11) 0.000
Female 10.83 (2.69) 0.000
Democratic vote share 84.16 (10.87) 0.000

Economic Magnitude Is Meaningful

Contextualising the 2.7 Point Effect

Benchmarks for Comparison

  • Male-Female gap: 10.8 points
  • Effect of one daughter: 2.7 points
  • Ratio: 25% of gender gap

Interpretation

  • Each daughter ≈ one-quarter the effect of legislator being female
  • Cumulative effect substantial:
    • 3 daughters vs 0 daughters: 8.1 points
    • About 75% of the gender gap

Economically significant effect, not just statistically significant

Treatment Heterogeneity

Male Legislators Show Stronger Response to Daughters

Differential Effects by Gender and Party

Heterogeneous treatment effects across subgroups

Effect concentrated among male legislators and Democrats

Males More Likely to Update Beliefs from Daughter Experience

Theoretical Explanation for Heterogeneity

Why Males Show Stronger Effects

  • Female legislators: Already exposed to women’s issues firsthand
  • Male legislators: Daughters provide new perspective
    • First direct experience with gender discrimination
    • Empathy through family member
    • Update priors more dramatically

Why Democrats Show Effects

  • Democrats: More freedom to vote ideology
    • Less party pressure on moral issues
    • Can respond to personal experiences
  • Republicans: Strong party discipline
    • Harder to break from party line
    • Though effect still positive (1.9 points)

Robustness: Multiple Measures

Effect Consistent Across Three Voting Indices

Different Organizations Weight Issues Differently

Robustness across NOW, AAUW, and RTL voting scores

All three measures significant at 5% level

Three Indices Capture Different Aspects of Women’s Issues

Measurement Strategy Builds Confidence

Index Organization Focus Effect p-value
NOW National Organization for Women 20 pieces of legislation 2.72 0.010
AAUW American Association of University Women 8 focused issues 2.63 0.019
RTL National Right to Life Committee Reproductive rights (reversed) 4.01 0.010

Consistent positive effects rule out measurement artifact

Reproductive Rights Show Strongest Effects

Issue Area Analysis

Why Reproductive Rights?

  1. Uniquely female issue: Directly affects daughters
  2. Moral dimension: Less party pressure
  3. Personal salience: Fathers consider daughter’s future

Evidence

  • RTL coefficient: 4.0 (largest effect)
  • Significance: \(p = 0.010\)
  • Interpretation: Each daughter increases liberal voting on abortion/contraception by 4 points

What We Have Learned Today

Five Key Lessons on Natural Experiments and Causal Inference

  1. Random assignment enables causal inference
    • Child gender is random in US (unlike China/India)
    • Balance tests verify no selection bias
  2. Proper controls are essential
    • Naive regression gives wrong sign
    • Controlling for total children reveals positive effect
  3. Economic magnitude matters
    • 2.7 points = 25% of male-female gap
  1. Treatment effects are heterogeneous
    • Stronger for males and Democrats
    • Supports mechanism: updating beliefs from experience
  2. Multiple measures build robustness
    • Consistent across NOW, AAUW, RTL
    • Strongest for reproductive rights

Next Week

Statistical Inference in Practice

From Estimation to Testing

  1. Hypothesis testing framework
    • Null vs alternative hypotheses
    • t-statistics and p-values
    • Type I and Type II errors
  2. Confidence intervals
    • Construction and interpretation
    • Relationship to hypothesis tests
  3. Joint hypothesis testing
    • F-tests for multiple restrictions
    • Testing economic theories with data
    • When individual tests aren’t enough

References

References

Warner, R. L. (1991). Does the Sex of Your Children Matter? Support for Feminism among Women and Men in the United States and Canada. Journal of Marriage and the Family, 53(4), 1051. https://doi.org/10.2307/353008
Warner, R. L., & Steel, B. S. (1999). CHILD REARING AS A MECHANISM FOR SOCIAL CHANGE: The Relationship of Child Gender to Parents’ Commitment to Gender Equity. Gender & Society, 13(4), 503–517. https://doi.org/10.1177/089124399013004005
Washington, E. L. (2008). Female Socialization: How Daughters Affect Their Legislator Fathers’ Voting on Women’s Issues. American Economic Review, 98(1), 311–332. https://doi.org/10.1257/aer.98.1.311